0=x^2-18x+23

Solution for 0=x^2-18x+23 equation:

0=x^2-18x+23

We move all terms to the left:

0-(x^2-18x+23)=0

We add all the numbers together, and all the variables

-(x^2-18x+23)=0

We get rid of parentheses

-x^2+18x-23=0

We add all the numbers together, and all the variables

-1x^2+18x-23=0

a = -1; b = 18; c = -23;
Δ = b2-4ac
Δ = 182-4·(-1)·(-23)
Δ = 232
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{232}=\sqrt{4*58}=\sqrt{4}*\sqrt{58}=2\sqrt{58}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-2\sqrt{58}}{2*-1}=\frac{-18-2\sqrt{58}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+2\sqrt{58}}{2*-1}=\frac{-18+2\sqrt{58}}{-2}
$